Select all of the equations below that are equivalent to: $\newline$ $20 = 14 + h$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $9 = 14 + h - 10$ $\newline$ (B) $15 = 14 + h - 5$ $\newline$ (C) $16 = 14 + h - 3$ $\newline$ (D) $2 = 14 + h - 17$

Full solution

Q. Select all of the equations below that are equivalent to:

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20 = 14 + h

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Use properties of equality.

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Multi-select Choices:

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(A)

9 = 14 + h - 10

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(B)

15 = 14 + h - 5

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(C)

16 = 14 + h - 3

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(D)

2 = 14 + h - 17

Original Equation: To determine which equations are equivalent to $20 = 14 + h$ , we need to manipulate the original equation using properties of equality to match the given choices. $\newline$ Let's start with the original equation: $20 = 14 + h$ .
Isolate $h$ : Subtract $14$ from both sides of the equation to isolate $h$ : $20 - 14 = 14 + h - 14$ . This simplifies to: $6 = h$ .
Check Choice (A): Now let's check each choice to see if it simplifies to $6 = h$ when we isolate $h$ . $\newline$ For choice (A): $9 = 14 + h - 10$ . $\newline$ Add $10$ to both sides: $9 + 10 = 14 + h$ . $\newline$ This simplifies to: $19 = 14 + h$ , which is not equivalent to $6 = h$ .
Check Choice (B): For choice (B): $15 = 14 + h - 5$ . Add $5$ to both sides: $15 + 5 = 14 + h$ . This simplifies to: $20 = 14 + h$ , which is equivalent to the original equation.
Check Choice (C): For choice (C): $16 = 14 + h - 3$ . Add $3$ to both sides: $16 + 3 = 14 + h$ . This simplifies to: $19 = 14 + h$ , which is not equivalent to $6 = h$ .
Check Choice (D): For choice (D): $2 = 14 + h - 17$ . Add $17$ to both sides: $2 + 17 = 14 + h$ . This simplifies to: $19 = 14 + h$ , which is not equivalent to $6 = h$ .